Question

By increasing the speed of a car by 10 km/hr, the time of the journey for a distance of 7
kom s reduced by 36 minutes. Find the orginal speed of the car.​

Answer 1

Correct Question:

By increasing the speed of the car by 10km/hr the time of journey for a distance of 72km is reduced by 36 minutes. Find the original speed of the car.

Answer:-

Given:

Distance covered by the car = 72 km

Let the original speed of the car be x km/h and the time taken by the car be y hrs.

We know that,

Distance = speed * time

Hence,

→ 72 = xy

→ 72/x = y -- equation (1)

Also given that,

The car increases its speed by 10 km/h and reaches the destination 36 mins earlier.

→ 72 = (x + 10) * (y - 36 min)

• 1 hr = 60 min
• 1 min = 1/60 hr.

→ 72 = (x + 10)(y - 36/60)

Substitute y value from equation (1).

⟶ 72 = (x + 10) * (72/x - 3/5)

⟶ 72 = x * (72/x - 3/5) + 10(72/x - 3/5)

⟶ 72 = 72 - 3x/5 + 720/x - 30/5

⟶ 72 - 72 + 6 = ( 720/x) - 3x/5

⟶ 6 = [ 720* 5 - 3x² ]/5x

⟶ 6 * 5x = 3600 - 3x²

⟶ 3x² + 30x - 3600 = 0

⟶ 3(x² + 10x - 1200) = 0

⟶ x² + 40x - 30x - 1200 = 0

⟶ x(x + 40) - 30(x + 40) = 0

⟶ (x - 30) * (x + 40)

• x - 30 = 0

→ x = 30

• x + 40 = 0

→ x = - 40

Speed cannot be negative. So, positive value is taken. i.e., 30 km/ hrs.

Therefore, the original speed of the train is 30 km/hrs.

Answer 2

Correct Question

• By increasing the speed of a car by 10 km/hr, the time of the journey for a distance of 72 km s reduced by 36 minutes. Find the orginal speed of the car.

GIVEN :-

• By increasing the speed of a car by 10 km/hr, the time of the journey for a distance of 72 km s reduced by 36 minutes

To FIND :-

• The Original Speed of car

SOLUTION :-

★ Let the original speed of car is x

★ The time taken it to cover 72 km = 72/x

$\underline{\bold{\bullet\:According\: to \:the\: Question :}}$

New time = 72/x + 10 hr

Difference in the time = 36 mins

72/x - 72/x + 10 = 36/60

x² + x - 1200 = 0

We get, x = - 40 or x = 30

Hence the original Speed of the car is

• 30 km/hr